Deconstructing zero: resurgence, supersymmetry and complex saddles

Understand

We explain how a vanishing, or truncated, perturbative expansion, such as often arises in semi-classically tractable supersymmetric theories, can nevertheless be related to fluctuations about non-perturbative sectors via resurgence.

• We also demonstrate that, in the same class of theories, the vanishing of the ground state energy (unbroken supersymmetry) can be attributed to the cancellation between a real saddle and a complex saddle (with hidden topological angle pi), and positivity of the ground state energy (broken supersymmetry) can be interpreted as the dominance of complex saddles.
• In either case, despite the fact that the ground state energy is zero to all orders in perturbation theory, all orders of fluctuations around non-perturbative saddles are encoded in the perturbative E(N, g).
• We illustrate these ideas with examples from supersymmetric quantum mechanics and quantum field theory.